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1, xt-1, , , , 15., , , , Sol. To find integral of Za, , , , : 1 il, Let integrand = —>—_,—, sr 1 DG ED, , Put x? = y only to form partial fractions., = ae = AL rs BL (i), ~ (y-Diy+D y-1” yeti ~, , Multiplying by L.C.M. = (y - 1 y + 1), 1=A(y+1)+Biy-1) or 1=Ay+A+By-B, Comparing coeffs. of y and constant terms, we have, , , , , , , , , , , , , , , , , , , , , , Coefficients of y: A+B=0 (ti), Constant terms A-Be=l1 «iti), 1, Adding (ii) and (iii), 2A = 1 => A= 2, Putting A= + in @i), 2 +B=0 ee, utting yo ee > = "9, Putting values of A, B and y in (i),, 1 1, 1 _ 2 __2, eA-1 0 ay P41, i Alen Ales, wy a) ype de 2 way, 11. x-1J 1. ,, = 921 1 xo] 5 tan xt+e, 1 1 x-a, P = ae = — 1, Jae 2a oe xta, , Note. Must put y = x” in (i) along with values of A and B before, writing values of integrals., Remark. Alternative solution is:, 1 1 1, x1 @=DO?+D (= Det DO? + D, , A B Cx+D, x-1 ° x+1 + P41, But the above given solution is better.